EGO with a failure region

from __future__ import annotations

import numpy as np
import tensorflow as tf

np.random.seed(1234)
tf.random.set_seed(1234)

The problem

This notebook is similar to the EI notebook, where we look to find the minimum value of the two-dimensional Branin function over the hypercube \([0, 1]^2\). But here, we constrain the problem, by adding an area to the search space in which the objective fails to evaluate.

We represent this setup with a function masked_branin that produces null values when evaluated in the disk with center \((0.5, 0.4)\) and radius \(0.3\). It’s important to remember that while we know where this failure region is, this function is a black box from the optimizer’s point of view: the optimizer must learn it.

import trieste


def masked_branin(x):
    mask_nan = np.sqrt((x[:, 0] - 0.5) ** 2 + (x[:, 1] - 0.4) ** 2) < 0.3
    y = np.array(trieste.objectives.Branin.objective(x))
    y[mask_nan] = np.nan
    return tf.convert_to_tensor(y.reshape(-1, 1), x.dtype)

As mentioned, we’ll search over the hypercube \([0, 1]^2\) …

from trieste.space import Box

search_space = Box([0, 0], [1, 1])

… where the masked_branin now looks as follows. The white area in the centre shows the failure region.

from trieste.experimental.plotting import plot_function_plotly

fig = plot_function_plotly(
    masked_branin, search_space.lower, search_space.upper
)
fig.show()